On the Kolmogorov constant in stochastic turbulence models

Stefan, Heinz G.

doi:10.1063/1.1514217

Cited by 20 publications

(18 citation statements)

References 15 publications

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“…[9][10][11] To apply ͑5a͒-͑5b͒, one has to parametrize G ik and C 0 . In accord with recent findings presented by the author, 5 one may set C 0 ϭ2.0. To calculate G ik , one may adopt the relationship between stochastic Lagrangian turbulence models and transport equations for Reynolds stresses.…”

Section: ͑2͒supporting

confidence: 70%

“…For an incompressible equilibrium turbulent boundary layer, for example, one finds r 32 ϭ(1.3, 1.5, 1.5) for friction Reynolds numbers Re ϭ(180, 395, 590), respectively. 5 Further, the influence of compressibility on r 32 seems to be very small, 6 such that the consideration of a constant r 32 appears to be an appropriate approximation under many conditions. A model that involves structural compressibility effects in addition to dilatational compressibility effects in supersonic turbulent reacting flow simulations does not exist at present.…”

Section: ͑2͒mentioning

confidence: 99%

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A model for the reduction of the turbulent energy redistribution by compressibility

Stefan

2003

Physics of Fluids

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Compressibility may strongly reduce the redistribution of turbulent kinetic energy. The question of how such effects can be taken into account in turbulence models is addressed here. First, a corresponding stochastic turbulence model is developed on the basis of a simplification of the generalized Langevin model for turbulent velocities. This model is then reduced to a deterministic model that extends existing methods by the consideration of structural compressibility effects. Combined with stochastic models for scalars, these velocity models may be used for compressible turbulent reacting flow simulations where the consideration of chemical reactions does not require approximations.

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Section: ͑2͒supporting

confidence: 70%

Section: ͑2͒mentioning

confidence: 99%

A model for the reduction of the turbulent energy redistribution by compressibility

Stefan

2003

Physics of Fluids

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“…Direct estimate of C 0 , which is essential in Lagrangian stochastic models of any order, [17][18][19][20] in either experiment or numerical simulation is difficult. Instead, the peak of the Lagrangian velocity structure function ͗⌬v() 2 ͘ when normalized by the dissipation rate ⑀ and time span , known as C 0 * , has been widely investigated.…”

Section: Introductionmentioning

confidence: 99%

Lagrangian statistics in turbulent channel flow

2004

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The Lagrangian dispersion of fluid particles in inhomogeneous turbulence is investigated by a direct numerical simulation of turbulent channel flow. Lagrangian velocity and acceleration along a particle trajectory are computed by employing several interpolation schemes. Among the schemes tested, the four-point Hermite interpolation in the homogeneous directions combined with Chebyshev polynomials in the wall-normal direction seems to produce most reliable Lagrangian statistics. Inhomogeneity of Lagrangian statistics in turbulent boundary layer is investigated by releasing many particles at several different wall-normal locations and tracking those particles. The fluid particle dispersion and Lagrangian structure function of velocity are investigated for the Kolmogorov similarity. The behavior of the Lagrangian integral time scales, Kolmogorov constants a 0 and C 0 of the velocity structure function near the wall are discussed. The intermittent behavior of the fluid particle acceleration is also examined by kurtosis of the Lagrangian structure function. Finally, the effect of the initial particle location on the dispersion is analyzed by the probability density function of particle position at several downstream locations.

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“…It was also observed that some anisotropy in the Lagrangian velocity structure function could be important in shear flows [25]. This was also considered in [26] where the effects of anisotropy together with acceleration fluctuations on the variations in C 0 (∞) were discussed. The choice for a constant value of C 0 is therefore questionable.…”

Section: Glm General Formulationmentioning

confidence: 93%

Generalised Langevin Model in Correspondence with a Chosen Standard Scalar-Flux Second-Moment Closure

Naud

Merci

Roekaerts

2010

Flow Turbulence Combust

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In the context of transported joint velocity-scalar probability density function methods, the correspondence between Generalised Langevin Models (GLM) for Lagrangian particle velocity evolution and Eulerian Reynolds-stress turbulence models has been established in the 1990's by S.B. Pope. It was shown that the GLM representation of a given Reynolds stress model is not unique. It was also shown that a given GLM together with a given mixing model for particle composition evolution implies a differential scalar-flux model. In this paper, we study how extra constraints can be applied on the choice of the GLM coefficients in order to imply a chosen scalar-flux model. This correspondence between GLM-implied and standard scalar-flux models is based on the linear relaxation term and on the mean velocity gradient contributions in the rapid term. In general, GLM-implied models possibly involve more terms (including anisotropy effects in the scalar-flux decay rate and some high-order terms in the rapid-pressure-scrambling term). The proposed form of the GLM supposes a non-constant value for the diffusion coefficient C0, originally identified as a Kolmogorov constant. Here, the value of C0 is determined in order to yield the Monin model for linear relaxation of the scalar-flux, and the constant in the rapid-pressure contribution is related to the choice of the parameter β in the GLM. We finally show how GLM-implied scalar-flux models are in general dependent on the choice of the mixing model and how the proposed GLM can reduce this dependency. These developments are illustrated by results obtained from calculations of the Sydney bluff-body stabilised flame HM1.Response to Reviewers: First of all, we would like to thank the reviewers for their comments which helped to improve the paper. #1We included all the suggestions of Reviewer #1. About remark 5: we used the more general formalism introduced by Wouters [REF. 4] that allows to deal with variable density flows, and with Reynoldsstress models that include cubic terms (we added a remark in the text after Equation (27) at the beginning of Section 4.1). #2The remarks of Reviewer #2 allowed us to distinguish more clearly in the text two aspects: 1. setting the C_0 value depending on the Monin linear relaxation term and 2. removing the effect of the mixing model as much as possible. This lead to some modifications of the text. The modification of β in order to be in agreement with Launder's model for the rapid-pressure-scrambling term is indeed pragmatic. We added some clarifications on this aspect on page 12 in the paragraph "Rapid-pressure-scrambling term". About the "philosophical questions" raised by the reviewer, here are some remarks on the modification of C_0 in order to lead the Monin linear return to isotropy (the main contribution of this paper). As mentioned by the reviewer "the scalar field is dynamically passive". With Taylor's hypothesis, we see the relation between the Monin constant and the GLM coefficient C_0. As discussed in the paper, there is no re...

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On the Kolmogorov constant in stochastic turbulence models

Cited by 20 publications

References 15 publications

A model for the reduction of the turbulent energy redistribution by compressibility

A model for the reduction of the turbulent energy redistribution by compressibility

Lagrangian statistics in turbulent channel flow

Generalised Langevin Model in Correspondence with a Chosen Standard Scalar-Flux Second-Moment Closure

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